61674 ÷ 6 = 10279 R0
We're going to perform division on 61674 with 6 as the divisor.

Step 1:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 6 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 2:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 3:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 12 from 16 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 6

Step 4:
6 goes into 47 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 1027
Subtract 42 from 47 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 6

Step 5:
6 goes into 54 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 10279
Subtract 54 from 54 to get 0.

The final result is 10279 with a remainder of 0.